Loan Interest Rate Calculator
Calculate the approximate interest rate of your loan based on the principal, total repayment, and loan term.
Estimated Annual Interest Rate
—Understanding Loan Interest Rate Calculation
This calculator helps you estimate the annual interest rate (APR) of a loan when you know the initial amount borrowed (principal), the total amount you have repaid (including principal and interest), and the duration of the loan in months.
The calculation is an approximation because it doesn't account for compounding frequency or potential fees that might be part of a real loan agreement. However, it provides a strong indication of the cost of borrowing.
The Math Behind the Calculation
The core idea is to determine the total interest paid, then use an iterative method or a financial formula to find the rate that makes the present value of the repayments equal to the principal. Since finding an exact algebraic solution for the interest rate (r) in the loan payment formula is complex, we often use an approximation or numerical methods.
For simplicity and to provide a quick estimate, this calculator uses an iterative approach. It calculates the total interest paid first:
Total Interest = Total Repayment - Loan Principal
Then, it estimates an average monthly interest amount:
Average Monthly Interest = Total Interest / Loan Term (Months)
This average monthly interest is then used to estimate the annual rate. A common simplified formula to approximate the annual interest rate (APR) is derived from the loan payment formula and rearranged. A widely used approximation formula for the annual interest rate (APR) is:
APR ≈ ( (Total Repayment / Loan Principal) - 1 ) * (12 / Loan Term in Months) * 100%
While this formula is a simplification, it gives a good first-order approximation. More precise calculations would involve financial functions like IRR (Internal Rate of Return) or specific loan amortization formulas, which are computationally more intensive.
Example Scenario
Let's say you took out a loan for $10,000 (Loan Principal). You agreed to repay a total of $11,500 over 36 months.
- Loan Principal: $10,000
- Total Repayment: $11,500
- Loan Term: 36 months
Using the formula:
APR ≈ ( ($11,500 / $10,000) - 1 ) * (12 / 36) * 100%
APR ≈ ( 1.15 - 1 ) * (1/3) * 100%
APR ≈ ( 0.15 ) * (0.3333) * 100%
APR ≈ 0.05 * 100%
Estimated Annual Interest Rate ≈ 5.0%
This means the loan effectively carries an annual interest rate of approximately 5.0%.
When to Use This Calculator
- To understand the true cost of a loan with a fixed repayment schedule.
- To compare different loan offers with varying total repayment amounts and terms.
- To check if the interest rate implied by a loan agreement seems fair.
Disclaimer: This calculator provides an estimated annual interest rate. Actual loan interest rates can be affected by fees, compounding periods, and specific loan terms not accounted for in this simplified model. Always refer to your loan agreement for exact details.